X-ray diffraction (XRD)

Solid matter can be described as being either amorphous, atoms arranged in a random way similar to the disorder found in liquids, or crystalline, atoms arranged in a regular pattern where a volume element (smallest in a material) that by repetition in three dimensions describes the crystal. This smallest volume element is called a unit cell, the dimensions of which are described by three axes: a, b, c and the angles between them alpha, beta, gamma (Figure 2.20) [90].

Figure 2.20: A unit cell with x, y, and z coordinate axes showing axial lengths (a, b, and c) and interaxiDODQJOHVĮȕDQGȖ>@

An electron in an alternating electromagnetic field will oscillate with the same frequency as the field. When an X-ray beam hits an atom, the electrons around the atom start to oscillate with the same frequency as the incoming beam. For amorphous materials, there will be destruc- tive interference in all directions, that is, the combining waves are out of phase and there is no resultant energy leaving the solid sample. However the atoms in a crystal are arranged in a regular pattern, and therefore yield constructive interference in some directions (Figure 2.21) [90].

Figure 2.21: (a) Demonstration of how two waves (labled 1 and 2) that have the same wave- length ȜDQGUHPDLQLQSKDVHDIWHUDVFDWWHULQJHYHQWZDYHV¶DQG¶FRQVWUXFWLYHO\LQWHUIHUH

with one another. The amplitudes of the scattered wave add together in a resultant wave. (b) Demonstration of how two waves (labeled 3 and 4) that have the same wavelength and become

out of phase after a scattering event (waves 3’ and 4’) destructively interfere with one another. The amplitudes of the two scattered waves cancel one another [90].

The waves will be in phase and there will be well defined X-ray beams leaving the sample. Hence, a diffracted beam may be described as a beam composed of a large number of scattered rays mutually reinforcing one another.

X-ray reflections originate from series of parallel planes inside the crystal: the orientation and interplanar spacing’s of these planes are defined by the three integers h, k, l called Miller indices. A given set of planes with indices h, k, l cut the a-axis of the unit cell in h sections, the b axis in k sections and the c axis in l sections (Figure 2.23). A zero indicates that the planes are parallel to the corresponding axis. E.g. the (2,2,0) planes cut the a– and the b– axes in half, but are parallel to the c– axis.

Figure 2.22: Example planes sections for respective h, k, l indices.

As mentioned, the indices values are used to calculate interplanar spacing dhkl, which for a

crystal structure of cubic symmetry for example, can be calculated according to Eq. (2.30).

in which a is the lattice parameter (unit cell edge length). The interatomic spacing, in conjunction with the angle of the diffracted beam and the incident wavelength upon the planes are related through Braggs law, Eq. (2.31).

Eq. (2.31)

where n is WKHRUGHURIUHIOHFWLRQZKLFKPD\EHDQLQWHJHU«FRQVLVWHQWZLWKVLQșQRW exceeding unity.

Powder XRD is one of the most widely used x-ray diffraction techniques for characteriz- ing materials. While samples are generally analyzed in powder form, consisting of fine grains of single crystalline materials, the technique is also used widely for studying particles in liquid suspensions or polycrystalline solids (bulk or thin film materials). As powder, the crystalline domains are randomly oriented in the sample, therefore when the 2-D diffraction pattern is recorded it shows concentric rings of scattering peaks corresponding to the various interatomic spacing’s in the crystal lattice. The positions and the intensities of the peaks are used for identi- fying the underlying structure (or phase) of the material. For example, the diffraction lines of graphite are different from diamond even though they both are made of carbon atoms. This phase identification is important because the material properties are highly dependent on structure. Likewise, the diffraction patterns for doped xerogels show a transition from amorphous to crystalline with heat treatment.

Figure 2.23: Xray diffraction of xerogels doped with 0.3% mol of europium and heat-treated at different temperatures displaying the transition from amorphous to crystalline material [91].

2.3.4 Raman Spectroscopy

Like XRD, Raman spectroscopy provides information on chemical structures and physi- cal forms to identify substances from the characteristic spectral patterns (“fingerprinting”). When light interacts with matter, the photons which make up the light may be absorbed or scattered, or pass straight through it without interacting. If the energy of an incident photon corresponds to the energy gap between the ground state of a molecule and an excited state, the photon may be absorbed and the molecule promoted to the higher energy excited state. It is this change which is measured in absorption spectroscopy by the detection of the loss of that energy of radiation from the light. However, it is also possible for the photon to interact with the molecule and scatter from it, in which case there is no need for the photon to have an energy matching the difference between two energy levels of the molecule. The scattered photons can be observed by collecting light at an angle to the incident light beam, and provided there is no absorption from any elec-

tronic transitions which have similar energies to that of the incident light, the efficiency increases as the fourth power of the frequency of the incident light [92].

Radiation is often characterized by its wavelength (ȜKRZHYHULQVSHFWURVFRS\WKHLQWe- raction of radiation with states of the molecule being examined are discussed in terms of energy, therefore frequenF\ȞRUZDYHQXPEHUȦDUHJHQHUDOO\XVHGDVWKH\DUHOLQHDUO\UHODWHGZLWK energy (E). The relationships between these scale are given in Eq. (2.32), Eq. (2.33), and Eq. (2.34).

Ȝ FȞ Eq. (2.32)

Ȟ ¨(K Eq. (2.33)

Ȧ ȞF Ȝ Eq. (2.34)

Energy is therefore proportional to the reciprocal of wavelength allowing characteristic intense scattering frequencies to be used as fingerprint values to determine or confirm the presence of various materials. An example of a Raman scattering for different carbon hydrides can be observed in Figure 2.24.

Figure 2.24: Raman scattering “fingerprints” for both acetone and ethanol.

2.3.5 Electrochemical measurement

Electrochemical measurements can be taken as “continuous” or “intermittent” by control- ling either the current or voltage, or both. Information can be collected by electrochemical measurement regarding chemical reactions taking place within battery electrodes and kinetic properties of battery components, which aid in explaining practical reaction voltages and charac- teristic discharge-charge behavior and deviation from theoretical performance. Typical testing procedures involve constant-current (CC) cycling or constant-current-constant-voltage (CCCV) cycling in order to understand electrochemical properties of cycling batteries. CC cycling requires that current remain constant for the duration of discharging and charging, but does not require that both the currents be equal. Likewise for CCCV cycling, but a voltage hold takes place at the upper cut-off voltage for a pre-set time interval or low current cut-off. Utilization of a voltage hold allows for equilibration of mobile species into an electrode.

One method of presenting and analyzing information is through use of discharge and charge curves, in which the cell voltage is plotted as a function of the state of charge. The

relationships for a single material can vary significantly depending upon the rate at which the energy is extracted from, or added to the cell. Likewise, curves vary extensively for different materials. Figure 2.25 shows an example of a discharge curve for various types of materials.

Figure 2.25: Schematic representation of three different types of discharge curves: one that is flat, one that has more than one flat curve, and a slanted/stretched S-shaped curve with a relative-

ly large slope [5].

The flat plateaus represent multiphase reactions with potentials that are essentially independent of the state of charge of the cell. A sloping plateau allows for potential misinterpretation as it could be the result of undesirable reactions between two or more components of the battery, such as the electrolyte and active material.

The information obtained from electrochemical measurements is not only limited to observation of reaction voltages, but is useful for observation of polarization losses (Chapter 4),

of materials (Chapter 6). Electrochemical measurements are also used to show cycle life through repeated cycling, and in the case of degradation, explain the mechanisms for reduced capacity (Chapter 4).

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3.

Solid Electrolyte

3.1 Introduction

Recent popularization of various kinds of portable electronic devices has driven the im- portance of energy devices like secondary batteries, fuel cells, and capacitors to new heights. It is widely understood that all-solid-state energy storage is most promising for improving safety and reliability of these devices [1]. As a key material of all-solid-state energy devices, solid electro- lytes have been extensively studied in the fields of materials science and electrochemistry. Many research efforts have focused on preparation of solid electrolytes with a broad spectrum of materials and manufacturing methods.

For any rechargeable lithium battery, the electrolyte material must permit the repeated

and rapid transfer of Li+between the anode and cathode over a predetermined set of operating

conditions (voltage, temperature, and current), without significant deterioration. Ideally, an electrolyte material would be electronically insulating, ultra-thin, lightweight, free of hazards and inexpensive. Inorganic solid electrolytes offer both advantages and disadvantages over liquid and

organic polymer electrolytes. For the required rapid transport of Li+ across the electrolyte, the

product of the resistivity and electrolyte thickness must be minimized (Ahrenius Equation,

In document Advances and Development of All-Solid-State Lithium-Ion Batteries (Page 74-102)